56. agrAhyah  
57. SASvatah
58. krsHNah
59. lohitAkshah
60. pradrdanah
61. prabhUtah
62. tri-kakud-dhAma

63. pavitram
64. mangalam param

  56. agrAhyah

One who is beyond the grasp of others.

The interpretation for this nAma by Sri Bhattar is that BhagavAn cannot be physically grasped, controlled, or acted upon by anyone or anything, and is thus beyond grasp.
He gives the following reference to the sruti:
nainam Urdhvam na tiryancam na madhye parijagrabhat -
One could grasp Him neither in the vertical dimension, nor in the horizontal dimension, nor in the third dimension, or for that matter, any other dimension.

Sri Sankara's interpretation is karmendriayih na grhyata iti agrAhyah - One who cannot be grasped by the organs of action. He gives the following reference to taittirIya upanishad - yato vAco nivartante, aprApya manasA saha - He cannot be described through speech, and cannot be reached by mind.

Sri ChinmayAnanda gives us yet another interpretation. He points out that the Lord is not the "object" of perception ever by any one, but He is the "subject" who perceives. Thus He is ever the Subject but never the object of perception. He is imperceptible and incomprehensible. Sri Chinmaya refers us to the kenopanishad passage:
"yat cakshushA na paSyati yena cakshUmsi paSyanti tadeva brahma tvam viddhi - Understand that Brahman is That which cannot be seen by the eyes,
but because of which eyes are perceiving other things.

57. shAshvatah

One who is eternal.

shASvat bhavatIti shAshvatah - That which remains the same at all times is the Permanent. Sri Bhattar points out that the fact that BhagavAn is SASvata is evident from the eternal flow of action pertaining to the world (i.e., creation etc.). Sri Chinmaya points out that for something to be permanent, it has to be changeless with time, and BhagavAn is the controller of time, and is not controlled or affected by time, and so is Eternal and permanent.

58. krShNaH

a) One who is always in a state of Bliss (with His sport of creation etc.).
b) One who has a dark-blue complexion..

The first interpretation is supported from the following verse in MahAbhArata -

krshir-bhU-vAcakah Sabdo NaSca nirvrti vAcakah |
vishNus-tad bhAvayogAcca krshNo bhavati SASvatah
|| (MB Udyogaparva 5.68.5)

Approximately translated, this says: kriShi means bhU, Na means nirvrtti or happiness and bliss, and BhagavAn is called KrShNa because He is the union of these two. Sri Sankara and Sri Bhattar interpret the name slightly differently with this same starting point. Sri Sankara interprets bhU to mean existence (bhU - bhav - to be), and Sri Bhattar interprets bhU to mean a receptacle or ground or container (e.g., bhUmi). So Sri Bhattar says that krShNa here means the receptacle of extreme joy because of His constant sport of creation etc. referred to in the previous nAma. Sri Sankara interprets the name to mean that He is the union of existence and bliss.

The second interpretation also has its support in the MahAbhArata -

krshAmi prthivIm pArtha bhUtvA kArshNAyaso halah |
krshNo varNaSca me yasmAt tasmAt krshNo'ham arjuna
|| SAnti parva 342.79

Note the words krshAmi, kArshaNa, and krshNa in the above. Each of these words leads to a new and different interpretation of the meaning of the nAma here. The meaning of the first line in the above sloka is "When the earth becomes shelled by its hard crust, I shall turn myself into an iron plough-share (black-coloured), and shall plough the earth." The name krshNa can arise out of the fact that He is doing the act denoted by the word "krshAmi". Sri Chinmaya beautifully points out that this "ploughing" refers to His ploughing all the stupidities in His devotees and preparing the heart-field, weeding out all the poisonous growth of sin, and cultivating therein pure Bliss.

The second part of the verse means "O Arjuna! Because of my dark complexion, I am called KrshNa". The dark complexion referred to above could be because He is the (dark colored) iron plough, or because He is dark complexioned like the water-bearing cloud. Either way, because of His dark complexion, He is called krshNa. Notice that the dark complexion is associated with "kAr mugil vaNNan" or "nIla megha syAmalan" - One who has the color of the rain cloud loaded with His limitless mercy.

Sri Chinmaya points out that the inner meaning behind the "dark" complexion is that BhagavAn is not easily recognized (i.e., He is veiled behind some darkness) by those who aspire to reach Him except through single-minded devotion.

The nAma krshNa can also be interpreted in terms of the word "AkarshaNa" or magnetic attraction. He is krshNa because He irresistibly attracts all His devotees. Or He sweeps away (like a magnet drawing away the iron filings) the sins in the hearts of those who meditate upon Him.

This nAma occurs once more later as nAma 554 in "vedAh svAngo'jitah krshNo.....". Sri Bhattar gives the meaning b) for nAma 554, and gives the first explanation for the current nAma describing the paravAsudeva form.

59.  lohitAkshah 

One with eyes red like the beautiful lotus flower.
Lohite akshiNi yasya sah lohitAkshah.

Sri Bhattar enjoys the beauty of this nAma by ascribing the redness in the eye to the supreme joy that BhagavAn has. One can recall the mantra "sa mA vrshabho lohitakshah sUryo vipaScit mansA punAtu", which we chant during our sandhyavandanam. This is the second reference so far to the beauty of BhagavAn's eyes (the earlier one was pushkarAksha).

While Sri Bhattar explains the redness of the eye as resulting from extreme joy, another explanation given is that the redness is a result of BhagavAn's anger towards the evil-doers, for the destruction of whom He takes the different avatAras - vinASAya ca dushkrtAm.

60. pradrdanah

The Destroyer.

This name is derived from the root tardih - to cause destruction. Pra-tarda means extreme destruction. Sri Bhattar gives the following from kaThopanisahd - yasya brahma ca kshtram ca ubhe bhavatah odanah - He who has for His food the brahmins and the kshatriyas (i.e., all beings of the universe) at the time of pralaya. Sri RadhAkrshNa Sastri points out that given the interpretation for this nAma, the redness of the eye in the previous nAma can be appropriately the result of anger at the time of dissolution.

61. prabhUtah

One who is affluent, ever full, and well-endowed with wisdom, greatness, and other qualities.

Literally, the word means "born full" pra-bhUta. Even though at the time of pralaya, BhagavAn destroys everything, still His affluence remains since He has the parama-pada (the transcendental world), which is full of Bliss. And His essential Nature, well-endowed with jnAna, bala, aisvarya, vIrya, Sakti, and tejas still remain. Even after reducing everything at pralaya, the vAmana can be the trivikrama.

62. tri-kakud-dhAma

There are three words in this name - tri, kakub or kakut, and dhAma

tri means three; kakub means the direction or quarter of a compass (for example); kakut means the hump (such as the hump on the back of a bull, or a peak or mountain); kakub and kakut also are interchangeably used for either meaning. dhAma means abode or residence, and also a ray of light or brilliance. Several interpretations arise depending on the choice of the meanings.

We will start with dhAma meaning brilliance. Sri Bhattar indicates that if this meaning is used, dhAma will have to be considered as a separate nAma. The first part is then interpreted as tri-kakut, which refers to the incarnation of BhagavAn as the varAha, the Boar with three horns. This interpretation for tri-kakut is supported by the following sloka from moksha dharma in the mahAbhArata -

tathaiva Asam tri-kakudo vArAham rUpam Asthitah |
trikakut tena vikhyAtah SarIrasya pramApaNAt || moksha dharma

"Then I assumed the form of a Boar with three horns. So I became known as 'tri-kakut'. With that form I killed the rAkshasa."

Sri Bhattar gives the above only as an alternative interpretation, but does not interpret the phrase tri-kakud-dhaAma as two separate words as explained above. Sri Sankara also interprets tri-kakub-dhAma as one nAma.

One interpretation Sri Bhattar gives for tri-kakud-dhAma is One who has as His abode parama-pada, which is thrice as large as this universe. An alternative interpretation given is that the three parts refer to the three groupings of the six guNas (jnAna, bala, aisvarya, vIrya, Sakti, tejas), and since He is the abode of these three groups of guNas, He is tri-kakud-dhAma.

Sri Sankara gives the interpretation that He is the base or support for the three regions of the entire space, the upper, the lower, and the middle, and therefore He is tri-kakud-dhAma.

Sri Chinmaya gives the vedAntic interpretation that He is the base or support for the three states of consciousness, viz., the jAgrat, svapna, and sushupti, and this is why He is called tri-kakud-dhAma.

63. pavitram 

Purity Incarnate.

Up to this point, the qualities, possessions, and body of BhagavAn have been portrayed step-by-step. Now we are passing to His essential Nature which is to be cognized through all of the above. The word is derived from pU - to purify. Either He is the Deity that purifies, or He is the means of purification. The purity referred to here is the inner purity of the mind, which He gives to those who meditate on Him.

Both Sri RadhAkrshNa Sastri and Sri Chinmaya offer a second and more uncommon interpretation - One who gives protection (trAyate) from the thunderbolt of Indra (pavi). Sri Chinmaya points out that in vedAnta indra refers to the mind (indriyANam rAjA indrah - the mind), and the thunderbolt of mind can destroy all the accomplishments of a sAdhaka, and uninterrupted medidation of Sri VishNu can give the protection against such distractions, and thus VishNu is pavi-tra.

64. mangalam param

The Embodiment of Supreme Auspiciousness

Sri Sankara quotes the following from VishNu PurANa -

aSubhAni nirAcashTe tanoti Subhasantatim |
smrti-mAtreNa yat pumsAm brahma tanmangalam viduh

"Brahman is known as beneficence because He wards off all evils and brings on a series of benefits to men on being merely remembered by them". 
emphasizes that He is the Supreme Beneficence. We may recall the introductory sloka 
"pavitrANAm pavitram yo mangalAnAm ca mangalam" by Bhishma; these two names occur now sequentially here.